"The condition of equilibrium is when the sum of the forces acting on a body is the zero vector. Suppose a body has a force of 2 pounds acting on it to the right, 5 pounds acting on it upward, and 3 pounds acting on it 45° from the horizontal. What single force is needed to produce a state of equilibrium on the body?"

The answer is pounds

Explanation:

We will start this question by representing the force vectors in Cartesian coordinate system:

Let the single force we need be represented by

Since, the body is in equilibrium the summation of all the forces acting on it should be zero:

∑ (Sum of all forces in direction is equal to zero)

( component of force 3 is negative because it is acting  in opposite direction)

∑ (Sum of all forces in direction is equal to zero)

( component of force 3 is negative because it is acting  in opposite direction)

So,

Hence, to get the scalar quantity of a single force:

pounds

true tan speed = ang vel x radius